The leader of Greenwich Council has said he has "no choice" but to ask schools to remain open after threats of legal action from the government.
The authority wrote to head teachers asking for classes to move online from Tuesday amid rising Covid-19 cases.
Education Secretary Gavin Williamson ordered the council to keep all schools open until the end of term.
Council leader Danny Thorpe said he could not justify using public funds to fight the decision in the courts.
In a statement, the Labour councillor said he did not agree that it was right to keep schools open but he had "no choice but to ask our schools to keep their doors open to all students, rather than just continuing with online learning".
Parents told the BBC it was an odd and confusing time for schools and families in the borough.
London, most of Essex and parts of Hertfordshire will move into England's highest tier of Covid restrictions on Wednesday due to a rise in infections.
Schools in England were told they could close a day early for Christmas last week to give staff a "proper break" from identifying potential coronavirus cases.
In Basildon, where the third-highest Covid rate was recorded, schools were also allowed to close early, while London's mayor Sadiq Khan has called on secondary schools and colleges in the capital to follow suit.
Imagine how baffling it's been for parents in Greenwich and other London boroughs caught up in this end-of-term playground power struggle - which has become a microcosm of the uncertainty about whether children should be in school this week.
On Sunday night Greenwich council told parents schools were moving online - and then on Monday, the Department for Education issued legal threats saying they would have to stay open.
And now on Tuesday, the council has backed down and says schools will have to stay open for Wednesday and Thursday.
It's added confusion to an already worrying time. Although parents will still be wondering what to believe when they're also being told to stay apart because of London's surge in Covid cases.
It might appear an unnecessary tussle about a couple of days in school. But it's been about who is in control and the government's determination not to see its biggest red line crumbling away - and that's keeping schools open.
Leaders at two other Labour-run local authorities - Waltham Forest and Islington - have also advised schools to move to online learning for the last few days of term amid rising Covid-19 rates in the capital.
Both councils told BBC London they were sticking by their decisions.
Schools Minister Nick Gibb has written to Islington and Waltham Forest asking them to reconsider. The BBC understands no legal action has been taken against the local authorities.
Mr Thorpe said on Friday there were 3,670 children self-isolating and 314 teaching staff, then on Monday an additional 580 children had to self-isolate.
This "exponential growth" in Covid-19 cases was the basis of his decision to ask schools to move to online teaching, he said.
"We are in a situation where the virus has been spreading quicker in Greenwich than it has done in other parts of London," he said.
"We had to make this call based on the data available to us. I find it regrettable the Secretary of State has pursued a legal route, as fundamentally my decision has been based solely on what is based for families here in Greenwich and not a courtroom battle.
"It shows the government think you can manage the pandemic response entirely from Whitehall and what we are saying is that we have different parts of London and different parts of the country that are experiencing difficult challenges."
Mr Thorpe said he made the decision "in the best interests of the people of Greenwich" but recognised the disruption that had been caused.
'Families really struggle'
One mother, who has two children at Halstow Primary School in Greenwich, said: "I really, really feel for schools because they've all worked so hard since September to have schools open to maintain education and that normality for kids.
"I don't know what the school is going to do now, whether they're going to say pupils need to go in or leave it for parents to make the decision. It's another day of poor schools making lots of decisions rather than focusing on our kids."
A father, whose children attend a different school in the borough, added: "It seems so odd that remote learning suddenly is no longer acceptable.
"I understand that some families will really struggle if parents cannot work from home. In Greenwich, we have never had numbers as bad as they are right now - I don't understand why relatively low impact options, such as online learning, are being taken off the table by the government."
Head of Ofsted Amanda Spielman described it as a "really difficult situation" in which people were "weighing up short-term concerns about health risks and long-term concerns about children's education".
She told BBC Radio 4's Today programme: "It's so easy to call for closures and forget the long-term price which children pay which our visits show so clearly.
"We've had children yo-yoing in and out of school through the autumn and really suffering as a result. We need clarity, consistency, not last minute decisions."
Mr Thorpe added that the Department of Health & Social Care had agreed that any resident could access a Covid-19 test, whether they were showing symptoms or not.
"This is a real step change from the current position and one that will benefit all of us locally," he added.
A head teacher's union has said many parents could still keep their children at home this week despite the government's stance.
Geoff Barton, general secretary of the Association of School and College Leaders (ASCL), said: "The government may find it has won a hollow victory in its squabble with Greenwich council over end-of-term arrangements.
"It has compelled direct classroom teaching for the last few days of term, but we would not be surprised if many parents simply keep their children at home given the evident concern over Covid infection rates.
"It has been an unseemly end to a gruelling and exhausting term when schools at the very least deserved some flexibility over their end-of-term arrangements in the best interests of their pupils and staff, but instead have been met with legal threats from the government."
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